1. The problem involves identifying the equations of lines from given points and matching them to graphs. 2. Given points: (4,0), (8,-5), (12,-10), (16,-15). 3. To find the equation of the line passing through these points, use the slope formula: $$m=\frac{y_2-y_1}{x_2-x_1}$$ 4. Calculate slope between (4,0) and (8,-5): $$m=\frac{-5-0}{8-4}=\frac{-5}{4}=-\frac{5}{4}$$ 5. Check slope between (8,-5) and (12,-10): $$m=\frac{-10-(-5)}{12-8}=\frac{-5}{4}=-\frac{5}{4}$$ 6. The slope is consistent, so the line equation is: $$y=mx+b$$ 7. Substitute point (4,0) to find $b$: $$0=-\frac{5}{4}\times4+b \Rightarrow 0=-5+b \Rightarrow b=5$$ 8. So the line equation is: $$y=-\frac{5}{4}x+5$$ 9. Compare with given options: - $y=-\frac{5}{2}x-4$ (not matching slope or intercept) - $y=\frac{7}{4}x+5$ (wrong slope) 10. The correct equation for the points is $y=-\frac{5}{4}x+5$, which is not exactly given. 11. For the graphs: - Graph B is downward sloping from top-right to bottom-left, matching negative slope. - Graph D is upward sloping from bottom-left to top-right, matching positive slope. 12. Therefore, Graph B corresponds to a line with negative slope like $y=-\frac{5}{4}x+5$. 13. Graph D corresponds to a line with positive slope like $y=\frac{7}{4}x+5$. Final answers: - Points line: $y=-\frac{5}{4}x+5$ - Graph B: downward slope line - Graph D: upward slope line